2164 search results for "regression"

Bivariate Linear Regression

August 13, 2015
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Bivariate Linear Regression

Regression is one of the – maybe even the single most important fundamental tool for statistical analysis in quite a large number of research areas. It forms the basis of many of the fancy statistical methods currently en vogue in the social sciences. Multilevel analysis and structural equation modeling are perhaps the most widespread and

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A glimpse on Gaussian process regression

August 11, 2015
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A glimpse on Gaussian process regression

The initial motivation for me to begin reading about Gaussian process (GP) regression came from Markus Gesmann’s blog entry about generalized linear models in R. The class of models implemented or available with the glm function in R comprises several interesting members that are standard tools in machine learning and data science, e.g. the logistic

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A glimpse on Gaussian process regression

August 11, 2015
By
A glimpse on Gaussian process regression

The initial motivation for me to begin reading about Gaussian process (GP) regression came from Markus Gesmann’s blog entry about generalized linear models in R. The class of models implemented or available with the glm function in R comprises several interesting members that are standard tools in machine learning and data science, e.g. the logistic

Read more »

Simple regression models in R

August 1, 2015
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Simple regression models in R

Linear regression models are one the simplest and yet a very powerful models you can use in R to fit observed data and try to predict quantitative phenomena. Say you know that a certain variable y is somewhat correlated with a certain variable x and you can reasonably get an idea of what y would be given x....

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Empirical bias analysis of random effects predictions in linear and logistic mixed model regression

July 30, 2015
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Empirical bias analysis of random effects predictions in linear and logistic mixed model regression

In the first technical post in this series, I conducted a numerical investigation of the biasedness of random effect predictions in generalized linear mixed models (GLMM), such as the ones used in the Surgeon Scorecard, I decided to undertake two explorations: firstly, the behavior of these estimates as more and more data are gathered for each

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Empirical bias analysis of random effects predictions in linear and logistic mixed model regression

July 30, 2015
By
Empirical bias analysis of random effects predictions in linear and logistic mixed model regression

In the first technical post in this series, I conducted a numerical investigation of the biasedness of random effect predictions in generalized linear mixed models (GLMM), such as the ones used in the Surgeon Scorecard, I decided to undertake two explorations: firstly, the behavior of these estimates as more and more data are gathered for each

Read more »

Regression with Multicollinearity Yields Multiple Sets of Equally Good Coefficients

July 6, 2015
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Regression with Multicollinearity Yields Multiple Sets of Equally Good Coefficients

The multiple regression equation represents the linear combination of the predictors with the smallest mean-squared error. That linear combination is a factorization of the predictors with the factors equal to the regression weights. You may see the wo...

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Heteroscedasticity in Regression — It Matters!

June 7, 2015
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Heteroscedasticity in Regression — It Matters!

R’s main linear and nonlinear regression functions, lm() and nls(), report standard errors for parameter estimates under the assumption of homoscedasticity, a fancy word for a situation that rarely occurs in practice. The assumption is that the (conditional) variance of the response variable is the same at any set of values of the predictor variables. … Continue reading...

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Simulation-based power analysis using proportional odds logistic regression

May 22, 2015
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Simulation-based power analysis using proportional odds logistic regression

Consider planning a clinicial trial where patients are randomized in permuted blocks of size four to either a 'control' or 'treatment' group. The outcome is measured on an 11-point ordinal scale (e.g., the numerical rating scale for pain). It may be reasonable to evaluate the results of this trial using a proportional odds cumulative logit

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Scale back or transform back multiple linear regression coefficients: Arbitrary case with ridge regression

April 10, 2015
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SummaryThe common case in data science or machine learning applications, different features or predictors manifest them in different scales. This could bring difficulty in interpreting the resulting coefficients of linear regression, such as one featur...

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